"One man's terrorist is another man's freedom fighter," as the saying – penned first by author Gerald Seymour in the 1975 thriller Harry's Game, and repeated ad nauseam since – puts it. Everything depends on your point of view. So what should we call the people who for the last four nights have been running riot in half-a-dozen British cities?

The BBC, for one, began last weekend by calling them "protesters", presumably because the initial rioting in Tottenham on Saturday was, or appeared to be, a protest at the lack of a satisfactory police response to questions about the death of Mark Duggan. It was a term the corporation continued to use for at least two further days, drawing a small storm of criticism from members of the public who took to Twitter to express their disapproval.

"Why do the press keep calling the rioters here protesters?" asked Linda Keen. "They're not protesting about or for anything."

Rob Steadman agreed: "This has nothing to do with protest."

In similar vein, Ed Gerstner demanded: "Seriously, @BBCnews, stop calling these people protesters. They're criminals, or rioters. But not protesters."

Amid accusations of political correctness and questions about whether the BBC considered "violence and looting" and "pure criminality" synonymous with legitimate protest, the corporation has insisted its reporters had also used the word "rioters", and that no guidelines had been issued – unlike in 2005, when head of news Helen Boaden circulated a memo in the wake of the 7/7 attacks on London warning that "the word 'terrorist' itself can be a barrier rather than an aid to understanding."

Some agreed it wasn't easy to choose the appropriate terminology. "They are suffering from high taxes, low income, unemployment and high prices ... Should they be called rioters or protesters?" tweeted one user. But the majority objected forcefully to the word protester, and many were not even happy with rioter. Dee Modha thought "thugs, hooligans and opportunists" would be better words, while Chris Sutcliffe, abandoning all niceties, urged everyone to "start using the correct word. Terrorists."

That may seem excessive. Choice of words very often implies a subjective judgement, as the Guardian's own style guide, on the word terrorists, points out. It adds: "We need to be very careful about using the term", and suggests alternatives – militants, radicals, separatists – that may sometimes be more appropriate.

The trouble is that one man's "excessive" may be another man's "appropriate". The style guide also cites the United Nation's definition of terrorism: "acts ... designed to create a state of terror in the minds of a particular group of people or the public as a whole for political or social ends". (The UN also makes clear that "having a good cause" makes no real difference). It is perfectly possible that some people on the receiving end of the most shocking violence in Croydon, Hackney, Ealing or Manchester would argue that fits their experience quite well.

The tabloids, in any event, have had few linguistic qualms. "Copycat cretins", was how Metro described the rioters on Wednesday. The Mirror opted for "gangs of mindless yobs", the Daily Mail "anarchists", and the Sun "morons", "thugs" and "idiots".

Numerous politicians have reached readily for "criminals", and David Cameron for "frankly sick". Nor have the public shied away from using their choice of words to vent their feelings: "Looters are scum" was the verdict emblazoned on the T-shirt of a woman helping with the clean-up in London.

But this week's unrest has thrown up other linguistic novelties. For example, "the feds" – an import from American crime shows – is now plainly the preferred term for the police, at least in many parts of London. "The feds are following me" was what Duggan texted to his fiancee, Semone Wilson, shortly before he died, and the word is everywhere on Twitter and Blackberry messenger (BBM). "Annoyed that the rioters call the police 'feds'," tweets Ben Liddell. "What happened to proper British nicknames like old bill, pigs and filth?"

A "bally" is a bandana or balaclava covering the face: "What ever ends your from put your ballys on link up and cause havic," was one BBM injunction.

"Mandem" or "man dem", originally Caribbean slang, has also become current in London, meaning friends: "The riots have begun ... mandem pullin out bats n pitbulls everywere. Join in!" was another BBM broadcast on Tuesday night. Language may sometimes betray; it also evolves.

• This article was amended on 12 August 2011 to make clear in the standfirst which term was causing controversy for the BBC.